Inequality

A mathematical statement that one quantity is greater than or less than another. " is less than " is denoted , and " is greater than " is denoted . " is less than or equal to " is denoted , and " is greater than or equal to " is denoted . The symbols and are used to denote " is much less than " and " is much greater than ," respectively.

Solutions to the inequality consist of the set , or equivalently .

Solutions to the inequality consist of the set , or equivalently . If and are both positive or both negative and , then .

The portions of the -plane satisfying a number of specific inequalities are illustrated above. Inequalities in two dimensions can be plotted using RegionPlot[ineqs, x, xmin, xmax, y, ymin, ymax].

Similarly, the portions of three-space satisfying a number of specific inequalities in the three Cartesian coordinates are illustrated above. Inequalities in three dimensions can be plotted using RegionPlot3D[ineqs, x, xmin, xmax, y, ymin, ymax, z, zmin, zmax].

The Wolfram Language command FindInstance[ineqs, vars] can be used to find a real solution of the system of real equations and inequalities ineqs in the variables vars or return the empty set if no such solution exists. Solution of inequalities can be performed using the command Reduce[ineqs, vars].

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